A New Administration. A New Era. But That Cake Looks Familiar.

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President Trump and Vice President Mike Pence cut a cake at the Salute to Our Armed Services inaugural ball on Friday. The cake was a replica of one made for President Barack Obama’s inauguration four years ago.CreditCreditChang W. Lee/The New York Times

Late Friday night, after a day of celebrations for President Trump’s inauguration, the pastry chef and TV personality Duff Goldman noticed something familiar: One of Mr. Trump’s three official inaugural balls — A Salute to Our Armed Services — featured a cake that looked exactly like one he had made for Barack Obama’s inauguration four years ago.

Mr. Goldman posted pictures on social media of the two cakes, both multilayered towers adorned by red, white and blue bunting, presidential seals and stars.

“The cake on the left is the one I made for President Obama’s inauguration 4 years ago. The one on the right is Trumps,” Mr. Goldman wrote. “I didn’t make it.”

The cake on the left is the one I made for President Obama's inauguration 4 years ago. The one on the right is Trumps. I didn't make it. 🤔 pic.twitter.com/qJXpCfPhii

On Saturday morning, the Buttercream Bakeshop, the bakery in Washington that made the cake for the Trump gathering, explained why the cake looked so similar to Mr. Goldman’s: The bakers had been asked by inaugural organizers to copy it.

On its Instagram account, the bakeshop wrote: “This year’s committee commissioned us to re-create it.”

“While we most love creating original designs, when we are asked to replicate someone else’s work we are thrilled when it is a masterpiece like this one,” the bakery wrote.

The inaugural cake quickly became a punch line on Twitter, a mock controversy with the hashtag #cakegate. And it was another intellectual property mishap, however small, connected to Mr. Trump. Earlier that day, Mr. Trump’s takeover of the @POTUS Twitter account included a stock image from Mr. Obama’s first inauguration that was used as its background.

The inauguration committee did not respond to an immediate request for comment.

A spokeswoman for Tiffany MacIsaac, the owner of Buttercream Bakeshop, said that some of the planners for the Armed Services ball approached the shop with a picture of the cake Mr. Goldman had made. The cake was largely for show, the spokeswoman said; it was made mostly of plastic foam, except for a portion at the bottom.

Buttercream Bakeshop donated its proceeds from the cake to the Human Rights Campaign, one of the nation’s largest L.G.B.T. civil rights advocacy groups and one of the bakery’s favorite charities.

Mr. Goldman did not respond to requests for comment. But as the story spread about how his cake was cloned, he posted a détente of sorts.

“Remembering a fantastic cake I made is awesome and the chef that re-created it for @POTUS Trump did a fantastic job. Group hug, y’all,” he wrote.

Mr. Goldman, who was featured on the Food Network’s cake-themed reality show, Ace of Cakes, told The Washington Post in 2009 that he hoped the cake he made for Mr. Obama would stay out of the news.

“The cake is only going to be the headline,” he said, “if it falls over on a senator or something like that.”